Intriguing challenges, risks, and functions for responsible behaviour in a system-technological and eco-social world are addressed from a methodological and ethical point of view. Various kinds and levels of responsibility are distinguished in terms of action (causal) responsibility, of task and role responsibility, and of universal moral and legal responsibilities well as from institutional and association perspectives. Some problems of ascribing, justifying, and distributing responsibility are discussed. Some professional codes of ethics in science and technology and characteristic responsibility conflicts are analysed, and 20 priority rules are proposed to help deal with or solve these important problems.